HCF of 546, 191, 145, 272 using Euclid's algorithm
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Want to know how to use Euclid’s algorithm to find the HCF of 546, 191, 145, 272 ? Well, you have come to the right place. In this article, you will be learning about Euclid’s algorithm and how to use it to calculate the HCF with ease.
Take the help of the HCF Calculator using the Euclid Division Algorithm which finds HCF of 546, 191, 145, 272 using Euclid's algorithm i.e 1 quickly.
Detailed Method to Find the HCF of 546,191,145,272 using Euclid's algorithm
Euclid’s algorithm is written as a = bq + r. This is known as the division lemma. The variable r varies according to 0 ≤ r ≤ b. We can use this to figure out the HCF of 546,191,145,272. This is how to do it.
Step 1: The first step is to use the division lemma with 546 and 191 because 546 is greater than 191
546 = 191 x 2 + 164
Step 2: Since the reminder 191 is not 0, we must use division lemma to 164 and 191, to get
191 = 164 x 1 + 27
Step 3: We consider the new divisor 164 and the new remainder 27, and apply the division lemma to get
164 = 27 x 6 + 2
We consider the new divisor 27 and the new remainder 2,and apply the division lemma to get
27 = 2 x 13 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 1.Therefore, the HCF of 546 and 191 is equal to 1
Notice that 1 = HCF(2,1) = HCF(27,2) = HCF(164,27) = HCF(191,164) = HCF(546,191) .
Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next
Step 1: The first step is to use the division lemma with 145 and 1 because 145 is greater than 1
145 = 1 x 145 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 1.Therefore, the HCF of 1 and 145 is equal to 1
Notice that 1 = HCF(145,1) .
Now, we must treat the HCF of the first two numbers as the next number in our calculation, and next
Step 1: The first step is to use the division lemma with 272 and 1 because 272 is greater than 1
272 = 1 x 272 + 0
As you can see, the remainder is zero, so you may end the process at this point. From the last equation, we can determine that the divisor is 1.Therefore, the HCF of 1 and 272 is equal to 1
Notice that 1 = HCF(272,1) .
Result
Hence, the HCF of 546, 191, 145, 272 is equal to 1.
FAQ on HCF of 546, 191, 145, 272 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid’s algorithm is represented as a = bq + r, and 0 ≤ r ≤ b..
2. How do you find HCF using Euclid's algorithm ?
Answer: Apply the division lemma to the numbers, and keep going until the remainder is zero. Once it becomes zero, the divisor will be your HCF.
3. What is the HCF of 546, 191, 145, 272?
Answer: The HCF of 546, 191, 145, 272 is 1.